Wild motivic McKay correspondence for arbitrary finite groups is proved via motivic integration over formal Deligne-Mumford stacks, yielding stringy motive invariance and a motivic Bhargava mass formula.
Moduli of formal torsors
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abstract
We construct the moduli stack of torsors over the formal punctured disk in characteristic p > 0 for a finite group isomorphic to the semidirect product of a p-group and a tame cyclic group. We prove that the stack is a limit of separated Deligne-Mumford stacks with finite and universally injective transition maps.
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Motivic integration over wild Deligne-Mumford stacks
Wild motivic McKay correspondence for arbitrary finite groups is proved via motivic integration over formal Deligne-Mumford stacks, yielding stringy motive invariance and a motivic Bhargava mass formula.